For which value of $k$, lines $x+2y=9$ and $kx+4y=-5$ are parallel?

Two lines are parallel when the coefficients of $x$ and $y$ are in the same ratio.

For $x+2y=9$ and $kx+4y=-5$,

$\dfrac{1}{k}=\dfrac{2}{4}$

$\Rightarrow 4=2k$

$\Rightarrow k=2$

The same thing using slopes: the first line has slope $-\dfrac{1}{2}$ and the second has slope $-\dfrac{k}{4}$.

$-\dfrac{k}{4}=-\dfrac{1}{2}$

$\Rightarrow k=2$